Document WO 2009/142482 discloses a second-stage drum for building tyres comprising a central shaft, a threaded shaft disposed on the central shaft and two half-drums. On both sides of the assembly defined by the two half-drums, a lead screw nut is coupled to the threaded shaft. Each lead screw nut is connected to the respective half-drum through a connecting element. Each half-drum is provided with a turning-up unit, comprising a turning-up lever, and a clamping unit for the bead core. The clamping unit is disposed on a cylindrical portion of the half-drum having a slot receiving the mentioned connecting element. The cylindrical portion further comprises a chamber inside which a pneumatic piston can move which is connected to the turning-up lever. The cylindrical portion is provided with a locking mechanism that can be engaged with or disengaged from the central shaft. When said locking mechanism is disengaged from the central shaft and a predetermined pressure is applied in the piston chamber, the clamping unit is integral with the turning-up lever and rotation of the threaded shaft involves axial movement of the whole half-drum. The two half-drums are moved close to each other to give the tyre a toroidal shape. When the locking mechanism is engaged on the central shaft and counter-pressure is applied in the piston chamber, rotation of the threaded shaft causes movement of the turning-up lever relative to the clamping unit and said turning-up lever moves upwards and towards the centre of the building drum to turn up the components of the tyre shaped around the bead core and against the sidewall.